Boston public schools will begin serving free lunches to all students this school year even if families have the financial means to pay, school officials are expected to announce Tuesday.

The meal program, more than a year in the making, is part of an experimental federal initiative that aims to make it easier for students from low-income families to receive free meals by eliminating the need to fill out paperwork, including potentially invasive questions about income.

Cities such as Atlanta, Detroit, and Chicago have been or will be participating in the free-meal program. Starting next school year, the program will be open to any school district across the country with high concentrations of students from low-income families. The cost of the free meals will be covered by the federal government.

“Every child has a right to healthy, nutritious meals in school, and when we saw a chance to offer these healthy meals at no cost to them, we jumped at the chance,” said Mayor Thomas M. Menino in a prepared statement. “This takes the burden of proof off our low-income families and allows all children, regardless of income, to know healthy meals are waiting for them at school every day.”

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The change, Boston school officials say, is a natural outgrowth of a decision last school year to offer all students free breakfasts. It eliminated an awkward socioeconomic divide that unfolded in some schools every morning, where low-income students would receive free milk, pastries, or other items in their classrooms, while more affluent students often went without.

At lunch, such a divide is generally less obvious because students use an ID card or a number when going through the cafeteria line, making it difficult for classmates to know whether meals are free or being charged to an account. In some cases, though, students pay with cash.

About three-quarters of Boston’s 57,000 students last year qualified for a free or a reduced-price lunch. A discounted lunch cost just 40 cents, compared with the full price of $2.25 in elementary schools and $2.50 in middle and high schools.

School officials say more students would have qualified for the perk if their parents had filled out an application.

Parents fail to do so for a variety of reasons, such as the forms being printed in a language they cannot read — more than 100 languages are spoken among Boston school families — or getting lost in a mountain of paperwork and notices that students bring home.

The problem can come with a steep financial price for families and the School Department alike.

Because many schools are reluctant to turn away students if they do not have the money, cafeteria workers charge the lunch to an account set up for the family. A principal or another school employee will eventually seek payment from parents or guardians — putting them in the awkward position of becoming bill collectors.

Last year, the School Department amassed $350,000 in losses from unpaid lunches, representing more than a third of the nearly $1 million that Boston sold in full- or reduced-priced lunches for the year. The loss had to be covered by other parts of the school budget, potentially diverting money from educational purposes.

“We are caught between a rock and a hard place,” said Michael Peck, the School Department’s director of food and nutritional services. “Many principals have told me, ‘The family doesn’t have the money; what do I do?’ ”

The US Department of Agriculture, which oversees school food programs, started experimenting with universal free breakfasts and lunches three years ago, as part of the 2010 Healthy, Hunger-free Kids Act, a centerpiece of Michelle Obama’s “Let’s Move!” initiative to end childhood obesity.

‘Many principals have told me, “The family doesn’t have the money, what do I do?” ’

To participate, a certain percentage of students in a district must qualify for free meals. That threshold — in light of the absence of student applications for free meals — is developed through a complex formula that includes such factors as the percentage of families in a community who receive food stamps.

Initially, the Agriculture Department selected only nine states and the District of Columbia to participate in the pilot program and Massachusetts was not among them. But Boston school officials pushed to add the state, achieving that goal this summer.

It remains unclear whether any other Massachusetts school districts will participate in the program this school year, but the state Department of Elementary and Secondary Education anticipates others could follow in the coming years.

“It definitely streamlines the process and reduces the time it takes for students going through the lunch line,” said Katie Millett, executive director for the Office of Nutrition, Health, and Safety Programs at the state’s Department of Elementary and Secondary Education. “I would think some of our larger districts will look at it.”

Boston school officials are hoping more students will eat the lunches now that they are free, instead of bringing something from home, setting a goal of a 10 percent to 20 percent increase in participation.

During the last school year, approximately 36,000 students — or 64 percent — ate a school-prepared lunch.

The Food Research and Action Center, an organization that promotes in-school meals, says more students have been taking advantage of the free lunches in other states that have begun the program.

The organization declined to release statistics because it will be putting out a report on the issue in the coming weeks.

“Whether those kids were packing lunches or doing without or running to a corner store — I don’t know,” said Madeleine Levin, senior policy analyst for the organization’s school breakfast and lunch program. “But more kids are eating the meals after this model is put into place. . . . It kind of levels the playing field and lets all kids get free meals without the stigma.”